666 jvbasha

javid basha jv

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5 years, 54 days

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These are replies submitted by 666 jvbasha

Dear @Carl Love 

Thanks for your reply.

I have tried for the n=1,2,3 like a round value; this is working. But when the values like 1.5 and 1.8, it is not executing.  
Kindly do the needful to find a solution 

Thank you.

Dear maple users 

Kindly do the needful to find a solution for the decimal power.

I am waiting for your reply

Thank you.

In this equation I have the numerator in decimal("^n-1")

It works when power("^n") is 1,2...and so on. 
But when power("^n") is decimal, like 0.8, 1.2, 1.4, it is not working.

Is there any way to tackle such a situation 

(1+(diff(f(x, t), x))^(n-1))*(diff(f(x, t), x))/(x*R(z)^2)+(diff(f(x, t), x))^(n-1)*(n-1)*(diff(f(x, t), x, x))/R(z)^2

Dear @acer 

I reworked the earlier question and found a new issue, so I made a new question.  

I am getting the following issue. I though It makes an Imaginary part.

unable to store HFloat(undefined)+HFloat(undefined)*I when datatype=float[8]
Is this possible to get a solution?

1.mw

restart:

with(LinearAlgebra):

with(PDEtools):

``

with(plots):

fcns := {f(x,t)};

{f(x, t)}

(1)

#GOLD

b1:=1.41:d:=0.5:xi:=0.1:ea:=0.5:c1:=1:eo:=0.2:c2:=1;tau:=0.5;m:=1.5:n:=0.8:ra:=1;alpha:=Pi/4;b2:=2:kappa:=Pi/4:

1

 

.5

 

1

 

(1/4)*Pi

(2)

 

 

 

R := proc (z) options operator, arrow; piecewise(d <= z and z <= d+1/2, 1-2*xi*(z-d), d+1/2 <= z and z <= d+1, 1+(-1)*.5*xi*(1+cos(2*Pi*(z-d-.5))), 1) end proc;

proc (z) options operator, arrow; piecewise(d <= z and z <= d+1/2, 1-2*xi*(z-d), d+1/2 <= z and z <= d+1, 1+(-1)*.5*xi*(1+cos(2*Pi*(z-d-.5))), 1) end proc

(3)

PDE1 :=-ra*tau*(diff(f(x,t),t))+b1*(1+ea*cos(c1*t))+b2*(cos(c2+kappa))+((m+(diff(f(x, t), x))^(n-1))/(x*R(z)*R(z))*diff(f(x, t), x)+(diff(f(x, t), x)/(R(z)*R(z)))*diff(m+(diff(f(x, t), x))^(n-1),x)+(1/(R(z)*R(z)))*(m+(diff(f(x, t), x))^(n-1))*diff(f(x, t), x$2));

PDE1 := -.5*(diff(f(x, t), t))+1.41+.705*cos(t)+2*cos(1+(1/4)*Pi)+(1.5+1/(diff(f(x, t), x))^.2)*(diff(f(x, t), x))/(x*piecewise(.5 <= z and z <= 1.000000000, 1.10-.2*z, 1.000000000 <= z and z <= 1.5, .95-0.5e-1*cos(2*Pi*(z-1.0)), 1)^2)-.2*(diff(f(x, t), x, x))/((diff(f(x, t), x))^.2*piecewise(.5 <= z and z <= 1.000000000, 1.10-.2*z, 1.000000000 <= z and z <= 1.5, .95-0.5e-1*cos(2*Pi*(z-1.0)), 1)^2)+(1.5+1/(diff(f(x, t), x))^.2)*(diff(f(x, t), x, x))/piecewise(.5 <= z and z <= 1.000000000, 1.10-.2*z, 1.000000000 <= z and z <= 1.5, .95-0.5e-1*cos(2*Pi*(z-1.0)), 1)^2

(4)

 

IBC := {D[1](f)(0,t)=0,f(1,t)=0,f(x,0)=0}:

z:=0.98:

 

sol1:=pdsolve(evalf({PDE1}),IBC ,numeric, time = t,spacestep = 0.025, timestep=0.001):
sol:=((evalf(Re(sol1))), output=listprocedure);

Re(sol1), output = listprocedure

(5)

p1 := (sol):-plot(f(x, t), t = 1.5,numpoints = 100);

Error, `sol` does not evaluate to a module

 

display([p1])

Error, (in plots:-display) expecting plot structures but received: [p1]

 

``

Download 1.mw

Hi maple users 

Is there any possibility of executing this code at sa=4?.
Kindly do the needful.
Thank for your help

Hi @tomleslie

I have found the results for sa=1 case, But it is not executing at sa=2 or 3 cases. 


Is there any way to get the solutions


Kindly do the needful.

badODEsys_(1).mw
 

  restart:
  with(plots):
  PDEtools[declare](f1(x),f2(x),f3(x), t1(x),t2(x),t3(x)):

f1(x)*`will now be displayed as`*f1

 

f2(x)*`will now be displayed as`*f2

 

f3(x)*`will now be displayed as`*f3

 

t1(x)*`will now be displayed as`*t1

 

t2(x)*`will now be displayed as`*t2

 

t3(x)*`will now be displayed as`*t3

(1)

  N :=1:
  F1:= add(p^jj*f1[jj](x), jj=0..N):
  F2:= add(p^jj*f2[jj](x), jj=0..N):
  F3:= add(p^jj*f3[jj](x), jj=0..N):
  T1:= add(p^jj*t1[jj](x), jj=0..N):
  T2:= add(p^jj*t2[jj](x), jj=0..N):
  T3:= add(p^jj*t3[jj](x), jj=0..N):

  gr:=5: pa:=5: sa:=1: br:=0.1: A1:=1: A2:=2: A3:=1:
  Eq11:= (1-p)*((diff(F1, x$2)+gr*T1)+pa)+p*((diff(F1, x$2)+gr*T1)+pa):
  Eq12:= (1-p)*(diff(T1, x$2))+p*((diff(T1, x$2)+br*(diff(F1, x))*(diff(F1, x)))):
  Eq21:= (1-p)*((diff(F2, x$2)+gr*A1*A2*T2)-sa*sa*F2+pa*A1)+p*((diff(F2, x$2)+gr*A1*A2*T2)-sa*sa*F2+pa*A1):
  Eq22:= (1-p)*(diff(T2, x$2))+p*((diff(T2, x$2)+A1*A3*br*((diff(F1, x))*(diff(F1, x))+sa*sa*F2*F2))):
  Eq31:= (1-p)*br*((diff(F3, x$2)+gr*T3)+pa)+p*((diff(F3, x$2)+gr*T3)+pa):
  Eq32:= (1-p)*br*(diff(T3, x$2))+p*((diff(T3, x$2)+br*(diff(F3, x))*(diff(F3, x)))):

  for i from 0 to N+1 do
      equ1[i] := coeff(Eq11, p, i) = 0:
      equ2[i] := coeff(Eq12, p, i) = 0:
      equ3[i] := coeff(Eq21, p, i) = 0:
      equ4[i] := coeff(Eq22, p, i) = 0:
      equ5[i] := coeff(Eq31, p, i) = 0:
      equ6[i] := coeff(Eq32, p, i) = 0:
  end do:

  con1[0]:= f1[0](-1) = 0, f1[0](0) = f2[0](0), D(f1[0])(0) = D(f2[0])(0),
            f2[0](1) = f3[0](1), D(f2[0])(1) = D(f3[0])(1),f3[0](2)=0:
  con2[0]:= t1[0](-1) = 0, t1[0](0) = t2[0](0), D(t1[0])(0) = D(t2[0])(0),
            t2[0](1) = t3[0](1), D(t2[0])(1) = D(t3[0])(1), t3[0](2)=1:
  for h to N do
      con1[h]:= f1[h](-1) = 0,  f1[h](0) = f2[h](0), D(f1[h])(0) = D(f2[h])(0),
                f2[h](1) = f3[h](1), D(f2[h])(1) = D(f3[h])(1), f3[h](2)=0:
      con2[h]:= t1[h](-1) = 0, t1[h](0) = t2[h](0), D(t1[h])(0) = D(t2[h])(0),
                t2[h](1) = t3[h](1), D(t2[h])(1) = D(t3[h])(1), t3[h](2)=0:
  end do:

  for i from 0 to N do
      P:= dsolve( {con1[i], con2[i], equ1[i], equ2[i], equ3[i], equ4[i], equ5[i], equ6[i]},
                  {f1[i](x), t1[i](x), f2[i](x), t2[i](x), f3[i](x), t3[i](x)}
                ):
      f1[i](x):=rhs(P[1]):
      f2[i](x):=rhs(P[2]):
      f3[i](x):=rhs(P[3]):
      t1[i](x):=rhs(P[4]):
      t2[i](x):=rhs(P[5]):
      t3[i](x):=rhs(P[6]):
  end do;

{f1[0](x) = -(5/18)*x^3-(10/3)*x^2+(5/36)*(31*exp(1)-38)*x/exp(1)+(5/36)*(-38+53*exp(1))/exp(1), f2[0](x) = -(95/18)*exp(x)/exp(1)-(35/36)*exp(-x)+(10/3)*x+25/3, f3[0](x) = -(5/18)*x^3-(10/3)*x^2+(50/9+(35/36)*exp(-1))*x+40/9-(35/18)*exp(-1), t1[0](x) = (1/3)*x+1/3, t2[0](x) = (1/3)*x+1/3, t3[0](x) = (1/3)*x+1/3}

 

-(5/18)*x^3-(10/3)*x^2+(5/36)*(31*exp(1)-38)*x/exp(1)+(5/36)*(-38+53*exp(1))/exp(1)

 

-(95/18)*exp(x)/exp(1)-(35/36)*exp(-x)+(10/3)*x+25/3

 

-(5/18)*x^3-(10/3)*x^2+(50/9+(35/36)*exp(-1))*x+40/9-(35/18)*exp(-1)

 

(1/3)*x+1/3

 

(1/3)*x+1/3

 

(1/3)*x+1/3

 

{f1[1](x) = (5/24192)*x^8+(5/756)*x^7+(805/15552)*x^6+(95/7776)*x^6*exp(-1)-(155/648)*x^5+(95/324)*x^5*exp(-1)+(24025/62208)*x^4-(14725/15552)*x^4*exp(-1)+(9025/15552)*exp(-2)*x^4-(5/6)*x^3*(47797/10368+(545/162)*exp(-1)-(95/1152)*exp(-2))-(5/2)*(69995/10368-(5/648)*exp(-1)+(13585/10368)*exp(-2))*x^2-(5/870912)*(7663012*exp(-1)*exp(1)-828590*exp(-2)*exp(1)-15854440*exp(-1)-2334780*exp(-2)+13548771*exp(1)-50721298)*x/exp(1)-(5/870912)*(7940828*exp(-1)*exp(1)-1310050*exp(-2)*exp(1)-15854440*exp(-1)-2334780*exp(-2)+11394973*exp(1)-50721298)/exp(1), f2[1](x) = -(1750/27)*x-(6125/1296)*x^4-211025/1296+10*(23609/3456-(155/81)*exp(-1)+(13585/10368)*exp(-2))*x+exp(-x)*(77709335/870912+(3325/256)*exp(-2)-(1415605/31104)*exp(-1))+(5/435456)*exp(x)*(7927220*exp(-1)+1167390*exp(-2)+25360649)/exp(1)-(475/54)*x^2*exp(x-1)+(175/108)*exp(-x)*x^2-(475/648)*x^4*exp(-1)-(950/81)*x^3*exp(-1)+(875/54)*x*exp(-x)-(9025/648)*exp(-2)*x^2-(40375/5184)*exp(-2)-(25/324)*exp(-1)-(5/216)*x^6-(5/9)*x^5+(9025/3888)*exp(2*x-2)+(1225/15552)*exp(-2*x)+(475/54)*x^2*exp(-1)-(1900/27)*x*exp(-1)-(875/81)*x^3+(875/108)*exp(-x)-(261025/2592)*x^2, f3[1](x) = (25/12096)*x^8+(25/378)*x^7-(175/7776)*x^6*exp(-1)+(475/972)*x^6-(175/324)*x^5*exp(-1)-(250/81)*x^5+(4375/1944)*x^4*exp(-1)+(6125/31104)*exp(-2)*x^4+(3125/486)*x^4-(5/6)*x^3*(125423/10368-(145/108)*exp(-1)-(5005/10368)*exp(-2))-(5/2)*(8539/1728+(785/162)*exp(-1)+(1645/576)*exp(-2))*x^2+(6375365/108864-(87101935/870912)*exp(-1)+(223525/20736)*exp(-2)-(3325/256)*exp(-1)*exp(-2)+(1415605/31104)*(exp(-1))^2)*x+(96778735/435456)*exp(-1)+(19625/31104)*exp(-2)-1711775/54432+(3325/128)*exp(-1)*exp(-2)-(1415605/15552)*(exp(-1))^2, t1[1](x) = -(1/432)*x^6-(1/18)*x^5-(805/2592)*x^4-(95/1296)*x^4*exp(-1)+(155/162)*x^3-(95/81)*x^3*exp(-1)-(4805/5184)*x^2+(2945/1296)*x^2*exp(-1)-(1805/1296)*exp(-2)*x^2+(47797/10368+(545/162)*exp(-1)-(95/1152)*exp(-2))*x+69995/10368-(5/648)*exp(-1)+(13585/10368)*exp(-2), t2[1](x) = -(1/432)*x^6-(1/18)*x^5-(1045/2592)*x^4-(95/1296)*x^4*exp(-1)+(5/162)*x^3+(95/27)*x*exp(x-1)+(95/54)*exp(x-1)-(95/81)*x^3*exp(-1)+(35/54)*x*exp(-x)+(35/12)*exp(-x)-(22805/5184)*x^2+(95/54)*x^2*exp(-1)-(1805/2592)*exp(2*x-2)-(245/10368)*exp(-2*x)-(1805/1296)*exp(-2)*x^2+(23609/3456-(155/81)*exp(-1)+(13585/10368)*exp(-2))*x+625/162-(1145/648)*exp(-1)+(6935/3456)*exp(-2), t3[1](x) = -(5/216)*x^6-(5/9)*x^5+(175/1296)*x^4*exp(-1)-(475/162)*x^4+(175/81)*x^3*exp(-1)+(1000/81)*x^3-(875/162)*x^2*exp(-1)-(1225/2592)*exp(-2)*x^2-(1250/81)*x^2+(125423/10368-(145/108)*exp(-1)-(5005/10368)*exp(-2))*x+8539/1728+(785/162)*exp(-1)+(1645/576)*exp(-2)}

 

(5/24192)*x^8+(5/756)*x^7+(805/15552)*x^6+(95/7776)*x^6*exp(-1)-(155/648)*x^5+(95/324)*x^5*exp(-1)+(24025/62208)*x^4-(14725/15552)*x^4*exp(-1)+(9025/15552)*exp(-2)*x^4-(5/6)*x^3*(47797/10368+(545/162)*exp(-1)-(95/1152)*exp(-2))-(5/2)*(69995/10368-(5/648)*exp(-1)+(13585/10368)*exp(-2))*x^2-(5/870912)*(7663012*exp(-1)*exp(1)-828590*exp(-2)*exp(1)-15854440*exp(-1)-2334780*exp(-2)+13548771*exp(1)-50721298)*x/exp(1)-(5/870912)*(7940828*exp(-1)*exp(1)-1310050*exp(-2)*exp(1)-15854440*exp(-1)-2334780*exp(-2)+11394973*exp(1)-50721298)/exp(1)

 

-(1750/27)*x-(6125/1296)*x^4-211025/1296+10*(23609/3456-(155/81)*exp(-1)+(13585/10368)*exp(-2))*x+exp(-x)*(77709335/870912+(3325/256)*exp(-2)-(1415605/31104)*exp(-1))+(5/435456)*exp(x)*(7927220*exp(-1)+1167390*exp(-2)+25360649)/exp(1)-(475/54)*x^2*exp(x-1)+(175/108)*exp(-x)*x^2-(475/648)*x^4*exp(-1)-(950/81)*x^3*exp(-1)+(875/54)*x*exp(-x)-(9025/648)*exp(-2)*x^2-(40375/5184)*exp(-2)-(25/324)*exp(-1)-(5/216)*x^6-(5/9)*x^5+(9025/3888)*exp(2*x-2)+(1225/15552)*exp(-2*x)+(475/54)*x^2*exp(-1)-(1900/27)*x*exp(-1)-(875/81)*x^3+(875/108)*exp(-x)-(261025/2592)*x^2

 

(25/12096)*x^8+(25/378)*x^7-(175/7776)*x^6*exp(-1)+(475/972)*x^6-(175/324)*x^5*exp(-1)-(250/81)*x^5+(4375/1944)*x^4*exp(-1)+(6125/31104)*exp(-2)*x^4+(3125/486)*x^4-(5/6)*x^3*(125423/10368-(145/108)*exp(-1)-(5005/10368)*exp(-2))-(5/2)*(8539/1728+(785/162)*exp(-1)+(1645/576)*exp(-2))*x^2+(6375365/108864-(87101935/870912)*exp(-1)+(223525/20736)*exp(-2)-(3325/256)*exp(-1)*exp(-2)+(1415605/31104)*(exp(-1))^2)*x+(96778735/435456)*exp(-1)+(19625/31104)*exp(-2)-1711775/54432+(3325/128)*exp(-1)*exp(-2)-(1415605/15552)*(exp(-1))^2

 

-(1/432)*x^6-(1/18)*x^5-(805/2592)*x^4-(95/1296)*x^4*exp(-1)+(155/162)*x^3-(95/81)*x^3*exp(-1)-(4805/5184)*x^2+(2945/1296)*x^2*exp(-1)-(1805/1296)*exp(-2)*x^2+(47797/10368+(545/162)*exp(-1)-(95/1152)*exp(-2))*x+69995/10368-(5/648)*exp(-1)+(13585/10368)*exp(-2)

 

-(1/432)*x^6-(1/18)*x^5-(1045/2592)*x^4-(95/1296)*x^4*exp(-1)+(5/162)*x^3+(95/27)*x*exp(x-1)+(95/54)*exp(x-1)-(95/81)*x^3*exp(-1)+(35/54)*x*exp(-x)+(35/12)*exp(-x)-(22805/5184)*x^2+(95/54)*x^2*exp(-1)-(1805/2592)*exp(2*x-2)-(245/10368)*exp(-2*x)-(1805/1296)*exp(-2)*x^2+(23609/3456-(155/81)*exp(-1)+(13585/10368)*exp(-2))*x+625/162-(1145/648)*exp(-1)+(6935/3456)*exp(-2)

 

-(5/216)*x^6-(5/9)*x^5+(175/1296)*x^4*exp(-1)-(475/162)*x^4+(175/81)*x^3*exp(-1)+(1000/81)*x^3-(875/162)*x^2*exp(-1)-(1225/2592)*exp(-2)*x^2-(1250/81)*x^2+(125423/10368-(145/108)*exp(-1)-(5005/10368)*exp(-2))*x+8539/1728+(785/162)*exp(-1)+(1645/576)*exp(-2)

(2)

 


 

Download badODEsys_(1).mw

 

Hi maple users,


Is there any way to get the solutions?
Kindly do the needful.

Hi @tomleslie 

I hope everything goes well

Is there any alter way to tackle the error

I have noticed one of your replaies, I have tried that one also.   I found the error.


Kindly look at one of your replaies

https://www.mapleprimes.com/questions/224981-Invalid-Subscript-Selector

Kindly do the needful to find a solution.
Thank you.

Dear @vv 

Many thanks for your reply.


Here we need to calculate the stream function. So should be calculated the integral constant values that time we can found the stream function.

Is this possible to found an integral constant(C1) value.

Dear @vv 

Thanks for your help.

Have a good day.

Dear @tomleslie 

Thanks for your explanation. Now I got clarity. I will cross-check the equation.

Have a good day.

Dear @tomleslie 

I have to calculate the values like 

L(0.71)=0 than f(x,t)=?

L(0.71)=0.1 than f(x,t)=?

..

L(0.71)=1 than f(x,t)=?.

and the x and t are 0.71 and 1.12.

But here various values of Z only the answer is coming.

The actual values are,

L(0.71)=0 than f(x,t)=0.5859

L(0.71)=0.1 than f(x,t)=0.5829

...

L(0.71)=1 than f(x,t)=0.

How to get the actual values.

Dear@Carl Love 

Thanks for the help

Have a good day.

Dear @Kitonum 

Thanks for the help

Have a good day.

Dear @tomleslie 

Thank you so much. 
I am would glad of your response.

Have a good day.

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